Semiglobal Observer-Based Non-Negative Edge Consensus of Networked Systems With Actuator Saturation

Composite Learning Adaptive Tracking Control for Full-State Constrained Multiagent Systems Without Using the Feasibility Condition

This article proposes a distributed consensus tracking controller for a class of nonlinear multiagent systems under a directed graph, in which all agents are subject to time-varying asymmetric full-state constraints, internal uncertainties, and external disturbances. The feasibility condition generally required in the existing constrained control is removed by using the proposed nonlinear mapping function (NMF)-based state reconstruction technology, and the Lipschitz condition usually needed in the consensus tracking is also canceled based on the adaptive command-filtered backstepping framework. The composite learning of the neural network-based function approximator (NN-FAP) and the finite-time smooth disturbance observer (DOB) provides a novel scheme for handling internal and external uncertainties simultaneously. One advantage of this scheme is that the use of online historical data of the closed-loop system strengthens the excitation of NN's learning. Another advantage is that the DOB with NN-FAP embedding realizes that the finite-time observation for external disturbance in the case of the system dynamics is unknown. A complete controller design, sufficient stability analysis, and numerical simulation are provided.

Bipartite Consensus for Second-Order Multiagent Systems With Matrix-Weighted Signed Network

The second-order scalar-weighted consensus problem of multiagent systems has been well explored. However, in some practical antagonistic interaction networks, the interdependencies of multidimensional states of the agents must be described by matrix coupling. In order to highlight the influence of matrix coupling in the antagonistic interaction network, we investigate the second-order matrix-weighted bipartite consensus problem on undirected structurally balanced signed networks. Under the proposed bipartite consensus protocol, an algebraic condition is obtained for achieving second-order bipartite consensus via utilizing matrix-valued Gauge transformation and stability theory. Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus. Besides, because of the existence of negative (positive) semidefinite connections, the matrix-weighted network may have clustering phenomena, which means that matrix weights play a critical role in achieving consensus. An algebraic graph condition for admitting cluster bipartite consensus is provided. By designing matrix weights in practical scenarios, the required number of clusters can be obtained. Finally, the theoretical results are verified by five simulation examples.

Further Improvements on Non-Negative Edge Consensus of Networked Systems

In this article, the non-negative edge consensus problem is addressed for positive networked systems with undirected graphs using state-feedback protocols. In contrast to existing results, the major contributions of this work included: 1) significantly improved criteria of consequentiality and non-negativity, therefore leading to a linear programming approach and 2) necessary and sufficient criteria giving rise to a semidefinite programming approach. Specifically, an improved upper bound is given for the maximum eigenvalue of the Laplacian matrix and the (out-) in-degree of the degree matrix, and an improved consensuability and non-negativevity condition is obtained. The sufficient condition presented only requires the number of edges of a nodal network without the connection topology. Also, with the introduction of slack matrix variables, two equivalent conditions of consensuability and non-negativevity are obtained. In the conditions, the system matrices, controller gain, as well as Lyapunov matrices are separated, which is helpful for parameterization. Based on the results, a semidefinite programming algorithm for the controller is readily developed. Finally, a comprehensive analytical and numerical comparison of three illustrative examples is conducted to show that the proposed results are less conservative than the existing work.

Distributed Adaptive Output Feedback Consensus of Parabolic PDE Agents on Undirected Networks

In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader-follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader-follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained.

Necessary and Sufficient Conditions of Formation-Containment Control of High-Order Multiagent Systems With Observer-Type Protocols

The analysis and design problems of formation-containment control for high-order linear time-invariant (LTI) multiagent systems (MASs) on directed graphs with observer-based output-feedback protocols are given in this work. To expand the feasibility of state formation configuration, two well-structured compensation signals are introduced for the leaders and followers in the protocols, respectively. Benefitting from the compensation signal of followers, the decoupling between formation control of leaders and containment control of followers is achieved. Thus, a necessary and sufficient condition is first established such that the formation-containment control for high-order LTI MASs can be achieved. Moreover, a heuristic iterative algorithm is developed to compute the controller gains, observer gains, as well as the compensation signals. Finally, two numerical examples are implemented to illustrate the time-varying formation-containment control of high-order MASs, which shows the validity and practicability of the theoretical results and algorithm.

Adaptive Anti-Disturbance Control for Systems With Saturating Input via Dynamic Neural Network Disturbance Modeling

This article discusses the issue of disturbance rejection and anti-windup control for a class of complex systems with both saturating actuators and diverse types of disturbances. At the input port, to better characterize those irregular disturbances, exogenous dynamic neural network (DNN) models with adjustable weight parameters are first introduced. A novel disturbance observer-based adaptive control (DOBAC) technique is then established, which realizes the dynamic monitoring for the unknown input disturbance. To handle the system disturbance with a bounded norm, the attenuation performance is concurrently analyzed by optimizing the L₁ gain index. Moreover, the PI-type dynamic tracking controller is proposed by integrating the polytopic description of the saturating input with the estimation of the input disturbance. The favorable stability, tracking, and robustness performances of the augmented system are achieved within a given domain of attraction by employing the convex optimization theory. Finally, using DNN-based modeling for three kinds of different irregular disturbances, simulation studies for an A4D aircraft model are conducted to substantiate the superiority of the designed algorithm.

Second-Order Consensus for Multiagent Systems With Switched Dynamics

This article investigates the consensus control problem for second-order multiagent systems with switched dynamics, consisting of a continuous-time subsystem and a discrete-time subsystem. Under a fixed directed topology, two linear control protocols are proposed for achieving consensus. One is that two subsystems use different control inputs, where the continuous-time system uses continuous-time control, and the discrete-time system uses discrete-time control. In order to reach consensus for this kind of control protocol, some necessary and sufficient conditions are derived. The other is to use the same control algorithm for the two subsystems, which is a sampled-data control input. Similar consensus conditions are also obtained. Finally, a few simulation examples are given to verify the theoretical results.

H∞ Control for Observer-Based Non-Negative Edge Consensus of Discrete-Time Networked Systems

This article is concerned with observer-based non-negative edge-consensus (OBNNEC) problems of networked discrete-time systems with or without actuator saturation. An algorithm which only uses actual outputs of neighboring edges is proposed by means of an H_∞ control method and modified algebraic Riccati equation (MARE)-based technique. The observer matrix and feedback matrix are constructed by solving the MARE and linear matrix inequality (LMI), respectively. Then, sufficient conditions for guaranteeing bounded inputs and non-negative edge states are derived. In addition, the low-gain characteristic of the MARE-based method is instrumental in guaranteeing non-negative edge states and deriving the feasible observer matrix and feedback matrix. Finally, two examples are shown to demonstrate the obtained theoretical results.

Adaptive Observer-Based Output Regulation of Multiagent Systems With Communication Constraints

In the absence of assuming that all agents know the system matrix of the external system, for heterogeneous linear multiagent systems (MASs), this article resolves the cooperative regulation problem in the presence of communication constraints. Based on the mild assumption on the digraph, two novel adaptive protocols are presented to solve the cooperative output regulation problem (ORP) via state feedback and measurement output feedback subject to snatchy and asynchronous information exchange between agents, unknown time-varying delays, and probable information losses. Finally, some simulations are offered to demonstrate the validity of our results about the problem.

Consensus of Second-Order Hybrid Multiagent Systems by Event-Triggered Strategy

In this article, an event-triggered method is proposed to solve the consensus of the second-order hybrid multiagent systems (MASs), which contain discrete-time and continuous-time individuals. First, we give a selection criteria of the coupling gains, the eigenvalues of communication topology, and the event-triggered sampling interval to guarantee the hybrid consensus, which have an impact on system stability, due to the interaction and co-existence of discrete-time and continuous-time individuals. Second, the hybrid second-order consensus under the event-triggered strategy is proven, where the agents communicate with their neighbors and update their controllers only at the triggered instants. Finally, we give some simulation examples to prove the validity of the main results.

Coordination Control for Uncertain Networked Systems Using Interval Observers

In this article, we take the coordination control problem of linear time-invariant networked systems with uncertain additive disturbance and uncertain initial states into consideration. A distributed interval observer is first constructed for uncertain networked systems in which the control algorithm of each agent involves only the upper bound information and the lower bound information of the interval observer associated with itself and its neighbors, respectively. With the help of the cooperativity theory, it is proved that the interval observer can estimate the piecewise state for each agent and the interval-observer-based control algorithm can drive the uncertain system to achieve coordination behavior. Then, time-varying coordinate transformation is introduced to construct a novel interval observer which can eliminate the cooperativity premise on the system matrices and bound the states of all agents in real time. It is shown that the novel interval-observer-based control algorithm can guide the uncertain system to reach coordinated behavior. Finally, the numerical simulations are provided to verify the theoretical results.